To be exact this swastika is not "Russian" but "Kalmuck". On this page you can see the facsimile of the order to the Kalmuck units of Red Army concerning the swastika on a uniform. The Kalmuck live in the south-east of the European Russia. This nation is of Mongol ancestry, their religion was lamaism. Very likely Bolsheviks thought that the sacral symbol would get Kalmucks to take part in Red Army as well as prevent their desertion from it. That is a rather usual practice for an ideology and religion of any kind... Anyway there are both a swastika and a five-pointed star on the arm-badge. View the translation of the facsimile into English below.

The city of Saratov, November 3, 1919

There be approved a distinctive arm-badge for the Kalmuck units, in accord with the draft and the description enclosed.
It is ordered to give the right of bearing the arm-badge to all the officers and Red Army men of the present and being organized Kalmuck units, in accord with the instructions of the order No. 116 given by the Republic Revolutionary Council of War this year.

A rhombus measuring 15 by 11 centimeters is made of red cloth. There are a five-pointed star in its upper corner and a garland in the center. There is a "LUNGTN"^* with the legend "R. S. F. S. R."^** in the center of the garland. The diameter of the star is 15 mm, that of the garland is 6 cm, the dimensions of "LUNGTN" are 27 mm, those of a letter are 6 mm.
The arm-badge for the officers and administrators is embroidered in gold and silver, while for Red Army men it is stencilled.
The star, "LUNGTN" and the ribbon of the garland are embroidered in gold (yellow paint for Red Army men), the garland itself and the legend are embroidered in silver (white paint for Red Army men).

Draft: (follows below)

^* Without any doubts this "LUNGTN" means a swastika, a fylfot, you see, but we don't know the etymology of this word. On the other hand it is written in capital letters, so the word looks like a kind of an abbreviation. Back
^** R. S. F. S. R. means Russian Soviet Federative Socialist Republic. Back

The information was taken from the journal Kommersant VLAST # 30 (381), August 1, 2000, p. 54. The original of the order is being kept in the Russian State War Archive.